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Regularity conditions for spherically symmetric solutions of Einstein-nonlinear electrodynamics equations | Alberto A. Garcia-Diaz
; Gustavo Gutierrez-Cano
; | Date: |
14 Nov 2019 | Abstract: | In this report, for static spherically symmetric (SSS) solutions of the
Einstein equations coupled to nonlinear electrodynamics (NLE) the regularity
conditions at the center are established. The NLE is derived from a Lagrangian
$mathcal{L}=mathcal{L}(mathcal{F})$, depending on the electromagnetic
invariant $mathcal{F}=F_{mu
u},F^{mu
u}/4$. Regular solutions are
characterized by the finite behavior at the center of the curvature invariants
of the Riemman tensor. For regular SSS metrics, the traceless Ricci (TR) tensor
eigenvalue $S$, the Weyl tensor eigenvalue $Psi_2$ and the scalar curvature
$R$ are singular--free at the center. Regular NLE SSS electric solutions, which
are characterized by the ${mathcal{F}}(r=0)=0$, approach to the flat or
conformally flat de Sitter--Anti de Sitter (regular) spacetimes at the center;
moreover, this family of solutions may exhibit different asymptotic behavior at
spatial infinity such as the Reissner--Nordtr"om (Maxwell) asymptotic, or
present the dS--AdS or other kind of asymptotic. Pure magnetic NLE SSS
solutions shear the single magnetic invariant $2mathcal{F}_m= h_0^2/r^4$, thus
they are singular in the magnetic field and may exhibit a regular flat or (A)dS
behavior at the center. | Source: | arXiv, 1911.6374 | Services: | Forum | Review | PDF | Favorites |
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